My guess is that simply recalling things you are happy about frequently has about the same effect as recalling things you are grateful for. I'm surprised none of those studies you cited attempted to disprove that. After all, things people are grateful for are often things that people are happy about and it's absolutely intuitive that if you recall things you're happy about a lot you'll be a happier person. If, however, they were indeed able to show that recalling things we're grateful for is more helpful than merely recalling things we are happy about, that would be a pretty significant discovery.

Ha. Yeah, I was also thinking about that as I was clearly writing a list of things that made me feel happy (not necessarily grateful).

I do think they use "happy about" and "grateful for" interchangeably. The main idea, as I interpret it, is to actually write those down so you have a record of how great life is. (Because I, at least, lose sight of that when going through a rough patch.)